Displacement convexity for the entropy in semi-discrete non-linear Fokker-Planck equations - Carrillo, JA; Jüngel, A; Santos, MC (Cambridge University Press, 2018)
The displacement λ-convexity of a non-standard entropy with respect to a non-local transportation metric in finite state spaces is shown using a gradient flow approach. The constant λ is computed explicitly in terms of a priori estimates of the solution to a finite-difference approximation of a non-linear Fokker-Planck equation. The key idea is to employ a new mean function, which defines the Onsager operator in the gradient flow formulation.